Math 234, Calculus for BusinessLecture 1, Textbook Sections 1.1, 1.2Lines, Supply and Demand, Revenue vs. CostJanuary 18th, 2017Print out these sheets to fill out during or after the lecture. They are for your own learning benefit!Announcements(1) Read the syllabus, and textbook Sections 1.1, 1.2. (2) Register on MyMathLab through the mainCompass site. (3) Contact me and your TA for all DRES accommodations immediately. (4) Contact me forall scheduling and exam conflicts immediately.Section 1.1, Linear FunctionsDefinition. A linear function isForms of Linear Functions Equation InterpretationQuestion 1. When are two lines parallel?Question 2. When are two lines perpendicular?Section 1.2, Linear Functions and ApplicationsSupply and DemandDefinition. The demand function isDefinition. The supply function isThe Law of Demand isThe Law of Supply is1Definition. Economic equilibrium occurs whenDefinition. The equilibrium quantity and price areThe Law of Supply AND Demand positsGraphically speaking, the equilibrium quantity q and price p areQuestion 3. What is the economic interpretation of D(q) < S(q)?Question 4. What is the economic interpretation of D(q) > S(q)?Example 1. Suppose supply and demand functions for math textbooks are given byp = S(q) =15q and p = D(q) = 120 −25qFind the equilibrium quantity and price.Solution. Step 1: Compute Equilibrium Quantity.The equilibrium quantity is .Step 2: Compute Equilibrium PriceThe equilibrium price is .Revenue vs. CostDefinition. The cost function isDefinition. The initial, fixed cost isDefinition. The marginal cost isDefinition. The revenue function isDefinition. The profit function is2Definition. The break-even point occurs whenDefinition. The break-even quantity isAn equivalent way to express the break-even point isExample 2. A carpenter sells tables at a price of $500 per table. Her initial cost to set up production is$30,000, and she requires $350 to construct each table. How many tables must she produce and sell to breakeven?Solution Step 1: Determine the Revenue and Cost functions. The revenue function isand the cost function isSolution Step 2: Solve R(x) = C(x)The carpenter must produce and sell tables to break-even.Example 3 (Follow-up to Example 2). How many tables must the carpenter produce and sell to profit by$6000?SolutionThe carpenter must produce and sell tables to profit by
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